The Reserve Bank of India (RBI) has asked state-run oil companies to buy dollars from a single bank, said a source privy to the advice from central bank, as the government struggles to stem the declining rupee.

The rupee fell to a record low of 61.21 against the dollar on Monday, exacerbating fears about the funding of the current account deficit and sending policy makers scrambling to find quick-fix solutions beyond sporadic interventions.

"We have been asked to buy dollars from a single bank. This order is for all IOC, HPCL and BPCL," said a source at one of the three companies.

The Reserve Bank of India met oil retailers on Monday to discuss options, including accessing dollars at market rates from a special window and routing dollar sales through a single bank, to ease pressure on the rupee.